Question

Derive the equation rate of change in momentum = force?

Answer 1

Answer:

P = m*v. Now, rate of change of momentum means change in momentum with respect to time is defined as force. F = dP/dt = d(mv)/dt. Now, momentum can be changed in a number of ways. Mass remains constant and velocity changes

Answer 2

Answer:

Let initial momentum ($p_i$) be mu

Let final momentum ($p_f$) be mv

According to 2nd law of motion

$\frac{p_f - p_i}{t} \propto \: f$

$\implies \: f \propto \frac{mv \: - mu}{t}$

$\implies \: f \propto \frac{m(v - u)}{t}$

$f \propto \: ma \: \: \: \: \: \: ( \frac{v - u}{t } = a )$

To remove the proportionality sign. We would add k as the proportionality constant

$f = kma \\ f = ma \:$

because by the definition of force k = 1